EEE 538 Homework 3

Due 26 April 16:30 in my mailbox

1. Consider a four link star voice network below where there is bi-directional  Poissonnian voice traffic between each pair of nodes. In the center of the star network, there is a transit node that does not originate or terminate any traffic. Assume all the link capacities the same and set to 100 circuits. Also assume that there are six classes, one for each pair of leaf nodes 1,2,3,4 and assume each pair brings the same amount of load say r erlangs where r = lambda/mu. Obtain the overall blocking probability

a) using the product form and calculating exactly the normalization constant

b) using the bound

c) using the reduced load approximation for

5 scenarios in which 3r = 85, 90, 95,100, and 105, respectively. Plot your results as a function of r and compare the methods a), b), and c).

2. Problem 3.40